Consider an orthogonal series [formula] where [formula] is an arbitrary orthonormal system for the interval (a, b) and [formula] is a sequence of real numbers. This report is a collection of theorems which give sufficient conditions for the convergence almost everywhere in (a, b) and summability a. e. in (a, b) of the above series.

There is an active principle in heparinized plasma that may be studied in vitro with a prescribed lipoprotein-containing medium. To this end the interaction of this active principle or factor was studied with lipoprotein species isolated from egg yolk.

A set of 69 pile yield curves for the production of plutonium, americium, and curium isotopes in a neutron flux of 5 x 10<sup>14 cm<sup>-2 sec<sup>-1 is given. The differential analyzer of the University of California Radiation Laboratory was used in obtaining the curves. The curves are given also on log-log plots for comparison.

The absolute excitation functions for the production of fission by charged particle bombardment in several substances were investigated at both high and low energies. The low energy work was done at the 60-inch Crocker cyclotron with alpha particles and deuterons, while the high energy work was done at the 184-inch cyclotron with alpha particles, deuterons, and protons.

The purpose of this note is to recalculate the semi-empirical curve of neutron yield vs. deuteron energy originally obtained by H. York in order to predict, using it and the best available data, what yields may be expected for deuterons on uranium in the extrapolated energy region.

The use of thermally fissionable material in the lattice adds a distributed source of fast neutrons which must be considered in evaluating the problem.

Project Sherwood is a nation-wide attempt to produce a controlled thermo-nuclear fusion reaction. The Astron experiment, conceived by Nicholas Christofilos, will utilize the effects of a cylindrical layer of relativistic electrons to contain and heat the plasma. A high quality, 200-ampere, 5-Me V electron beam is required to form the electron layer. The electron beam is produced by a linear induction electron accelerator. Three hundred and thirty-three toroidal cores of magnetic material surround an evacuated ceramic accelerating column. The electrons are accelerated by the transverse electric field produced by the changing flux. The magnetic cores are tape-wound toroids of .001", 50% Ni - 50% Fe. Two hundred eighty-eight cores are 24" o.d. x 8-1/2" i. d. x 1/2" thick and the remaining forty-five are 33" o. d. x 18" i. d. x 1/2" thick. Each core is required to support 16 kG for 0.4 psec. The choice of magnetic material was made by testing all available material for the required parameters. Results of these tests are presented.

The basic investigation of transistor feedback amplifiers has proven mathematically simple and of great practical value. The behavior of single-stage common-emitter amplifiers is described and provides a building block with which cascaded feedback amplifiers can be analyzed and designed. From the results of this analysis the conditions for minimum drift for cascaded single-stages and cascaded loops have been derived.

The method of detecting unpaired electrons in liquid and solid systems by electron spin resonance is discussed. The significance of the hyperfine structure in electron spin resonance is discussed and the possible use of these structural features of the electron spin resonance spectrum to elucidate the nature of the photoproduced unpaired electrons in photosynthesizing systems is introduced.

The kinetic energies of pions from radioactive decays in propane have been determined by using the information given by the angles of the secondary particles. This method is independent of any range-energy relation.

The oscillator of the 88-in. cyclotron which is being built in Berkeley is tunable from 5.3 to 16.5 Mc. It delivers a maximum c-w power of 300 kw. At the rated doc voltage of 75 kv the resonator stores 4.5 joules of electrical energy. The transients produced by this amount of energy, during sparking, place unusual requirements upon the design of the oscillator tube. The features of the RCA 6949 which make it particularly well-suited to this type of application are discussed in this paper. Other topics covered are the oscillator anode power supply, the hard-tube modulator, protective equipment, and oscillator instrumentation.

This report is an outgrowth of the MURA Users' Conference of June 1959. At that conference the group on beam separators discussed the problem of whether particle separation could be achieved at the machine energies under consideration. A preliminary version of the scheme outlined here was given at the conference. Later, after flaws were discovered, it was modified. The attempt is not to show that this is the way it should be done, but to show with reasonable certainty that there is at least one way it can be done.

A preliminary investigation of four types of multiplier phototubes under conditions simulating their use in scintillation and Cerenkov nuclear detectors is described. The investigation involves time-spread and rise-time measurements at different reference points on the outpost pulses, as well as observations of some special characteristics of these tubes.

Summary of research progress meetings of October 2 and October 9, 1952: High speed high vacuum ion pump, High energy ion irradiation, Space charge accelerator for protons, Availability of the [ ] meson beam at the cyclatron, Effect of chemical structure on stopping powers for high energy protons.

The theory of the hydrodynamic origin of cosmic rays proposed by Johnson and the author (Colgate) has developed to the point where the final evolution of a star to the supernova instability and subsequent explosion can be described with sufficient detail such that cosmic rays with appropriate intensity, composition, and spectrum to account for observations are a logical and necessary result. In the first publication it was pointed out that nuclei in the surface of the star may acquire many orders or magnitude more than the average energy per particle released in the explosion because of the large ratio of matter density between the core and the outer mantle. A shock from a sudden pressure increase in the core intensifies as it advances into lower-density material, thereby imparting extreme relativistic energies to the outermost layers. The shock wave was assumed on the basis that the observed explosion occurred in a time short compared to the traversal time of sound across the dimensions of the star. It was argued without proof that an adiabatic process would be inconsistent with the accepted gravitational instability as the trigger mechanism. In an attempt to confirm this supposition we extend the hydrodynamic calculations to describe …

This scaler was designed to replace an obsolescent tube design that was in general use at Lawrence Radiation Laboratory in Livermore. The new design, using solid state devices and printed circuit modules, allows two complete scalers in one frame to occupy the same rack space as the tube design. Switches in the input circuits of the new scaler change input impedance and sensitivity for operation with either tube or transistor circuits. The use of transistors has greatly increased reliability, and has also reduced power by a factor of fifteen. Modular construction of all circuits, including the power supply, minimizes down time since all modules are replaceable without removing the scaler from its rack. Reliability, then cost, were the criteria dictating choice of components and circuits in the scaler design.

Several investigators have found that the resistance to heat transfer at certain metal-metal interfaces is dependent upon the direction of heat flow across these interfaces. This paper shows that such a phenomenon can be explained by application of the theory of heat conduction in the solid state.

Recoil ranges of C11 from the reaction C12(p,pn)C11 are presented for incident proton energies from 0.25 to 6.2 Gev. From these data it is concluded that a neutron evaporation mechanism cannot be the major mechanism. The result for incident energies of 3 and 6.2 Gev are consistent with a fast reaction consisting of a single inelastic nucleon-nucleon collision. Assuming this mechanism, an average kinetic energy of 19 Mev can be deduced for the struck neutron (before the collision) in the C12 nucleus.

A systematic study is made of the electromagnetic properties of charged vector mesons. The various formalisms used to describe charged particles of spin 1 are compared, and a new first-order formulation of the Stuckelberg theory is developed.

Of the saturated hydrocarbons, isobutane represents the simplest case where specificity in radiolytic behavior owing to structural configuration should be apparent. The hydrogen bonded to the tertiary carbon atoms should, on the basis of bond strengths alone, be expected to be more reactive than other hydrogen atoms in the molecule. In order to investigate such specificity, liquid isobutane has been irradiated at 20' and an attempt made to identify and measure all products through the C8 (C<sub>8) hydrocarbons.